{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BS4AJU3UUDDGTYPFYKYJ4E2RO5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3ce45164e1a8beb0166093e94398bfd7f06739ab4e6d9e083c8955162d745136","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-17T15:49:53Z","title_canon_sha256":"e2a4d19d663ef0377154d2fbfd4b2b482643f7f56b8d21639d08e4efdbcc19f2"},"schema_version":"1.0","source":{"id":"2506.14656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.14656","created_at":"2026-07-05T11:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.14656v1","created_at":"2026-07-05T11:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14656","created_at":"2026-07-05T11:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"BS4AJU3UUDDG","created_at":"2026-07-05T11:27:47Z"},{"alias_kind":"pith_short_16","alias_value":"BS4AJU3UUDDGTYPF","created_at":"2026-07-05T11:27:47Z"},{"alias_kind":"pith_short_8","alias_value":"BS4AJU3U","created_at":"2026-07-05T11:27:47Z"}],"graph_snapshots":[{"event_id":"sha256:478833cd76ce2ce219f080552f49af5a12e09ce1267a5b21e944b8453254c203","target":"graph","created_at":"2026-07-05T11:27:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.14656/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the mean value of the twisted second moment of primitive cubic $L$-functions over $\\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \\begin{equation*} \\sum_{\\substack{\\chi\\ primitive\\ cubic\\\\ genus(\\chi)=g}}\\chi(h_1)\\bar{\\chi}(h_2)|L_q(\\frac{1}{2}, \\chi)|^2, \\end{equation*} where $L_q(s,\\chi)$ denotes the $L$-function associated with primitive cubic character $\\chi$. Employing a double Dirichlet series approach, we establish an error term of size","authors_text":"Zhiyong Zheng, Ziwei Hong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-17T15:49:53Z","title":"Twisted second moment of primitive cubic L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14656","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:387cb69cef9cc4b88abd0a401de47f0f4c221a22711d9907e0fb7ed66e685a58","target":"record","created_at":"2026-07-05T11:27:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3ce45164e1a8beb0166093e94398bfd7f06739ab4e6d9e083c8955162d745136","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-17T15:49:53Z","title_canon_sha256":"e2a4d19d663ef0377154d2fbfd4b2b482643f7f56b8d21639d08e4efdbcc19f2"},"schema_version":"1.0","source":{"id":"2506.14656","kind":"arxiv","version":1}},"canonical_sha256":"0cb804d374a0c669e1e5c2b09e1351777fee3f41fec79c54099b86f0d06680cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cb804d374a0c669e1e5c2b09e1351777fee3f41fec79c54099b86f0d06680cf","first_computed_at":"2026-07-05T11:27:47.707093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:47.707093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SEc3ue0CYEgFIcVLwbDgTcee5D2LTJEsytJJ0boCYxeQFik4PZdW57vIGnVU5yvPqpQkhmU70vRDK/PG4zD5AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:47.707581Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.14656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:387cb69cef9cc4b88abd0a401de47f0f4c221a22711d9907e0fb7ed66e685a58","sha256:478833cd76ce2ce219f080552f49af5a12e09ce1267a5b21e944b8453254c203"],"state_sha256":"ebab3a149d1a8c95b3dd7e467d462af36dc85d4d9e2c3b0ff6f461427f7c6c8f"}